Preheat the oven to 400°F. Arrange the biscuit dough on one side of a baking sheet and the sausage patties on another. Bake until the biscuits are golden brown and sausages are heated through, 10 to 12 minutes.
While the biscuits and sausages are baking, cut each slice of cheese into quarters. Split the warm biscuits in half and lay a cheese quarter over the bottom of each biscuit. Top with a sausage patty and the biscuit top and serve immediately.